Approaching a twin primes conjecture proof

From: James Harris (jstevh_at_msn.com)
Date: 06/29/04 

Date: 29 Jun 2004 14:55:14 -0700

The twin primes conjecture is that there are an infinity of twin
primes which are primes separated by 2. For instance, 5 and 7 are
twin primes, as 7-5 = 2.

Here's an idea that's a variant on the proof of the infinitude of
primes, might not be new, but why not throw it out there?

Multiply every prime *except* 3 up to some arbitrary j-th prime. Now
add 1.

The result is either divisible by 3 or has a residue of -1 or 1 with
respect to 3.

If the result is not divisible by 3 it is prime.

If the result is has a resdiue of -1, then when you add 2 to it, the
result is prime, so you have a paired prime.

Now then, all you have to do is prove that there will be a continuous
cycling between possibilities of 0, -1 and 1 residues with respect to
3.

Example:

2(5) = 10 + 1 = 11 = -1 mod 3, and 13 is prime

Now then, someone out there who wants worldwide fame in math circles
just needs to prove that you will always find a product P of a series
of primes with 3 left out such that P = -1 mod 3.

Have fun!

James Harris

Relevant Pages

  • Re: twin prime conjecture
    ... mistake that is commonly made regarding the density of primes (just do ... Let's look at the twin pairs in the range 114 to 126 ("twin pair" is my ... of density of twin primes and I will be glad to update the proof. ... probability argument when in fact I am not. ...
    (sci.math)
  • twin primes and goldbach conjectures unprovable?
    ... prove that the Twin Primes Conjecture and Goldbach's Conjecture ... equivalent to showing that $S \cap T$ is infinite. ...
    (sci.math)
  • Re: an true information theory
    ... > The basic idea is that if the correct algorithm is A, ... But you mentioning primes jogged ... for finding Mersenne primes is an example, or could be, ... are infinitely many twin primes (this is the twin prime conjecture, ...
    (sci.math)
  • Re: Approaching a twin primes conjecture proof
    ... > The twin primes conjecture is that there are an infinity of twin ... I kept thinking, "Twin primes? ... but the remainder can be 1. ...
    (sci.math)
  • Re: twin prime conjecture
    ... mistake that is commonly made regarding the density of primes (just do ... Let's look at the twin pairs in the range 114 to 126 ("twin pair" is my ... relatively prime to 2,3,5,7,11 is equal to the total number of twin ... of density of twin primes and I will be glad to update the proof. ...
    (sci.math)